We report a μSR study on the antiperovskite oxide superconductor Sr3-xSnO. By using transverse-field μSR, we observed an increase of the muon relaxation rate upon cooling below the superconducting transition temperature Tc = 5.4 K, evidencing bulk superconductivity. The exponential temperature dependence of the relaxation rate σ at low temperatures suggests a fully gapped superconducting state. We evaluated the zero-temperature penetration depth λ(0) ∝ 1/√σ(0) to be around 320-1020 nm. Such a large value is consistent with the picture of a doped Dirac semimetal. Moreover, we established that the ratio Tc/λ(0)-2 is larger than those of ordinary superconductors and is comparable to those of unconventional superconductors. The relatively high Tc for small carrier density may hint at an unconventional pairing mechanism beyond the ordinary phonon-mediated pairing. In addition, zero-field μSR did not provide evidence of broken time-reversal symmetry in the superconducting state. These features are consistent with the theoretically proposed topological superconducting state in Sr3-xSnO, as well as with ordinary s-wave superconductivity.